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Y=-4x

Y=3x+28
Solve by substitution

1 answer

To solve the system of equations using substitution, we'll follow these steps:

  1. Solve one of the equations for one variable.
  2. Substitute that expression into the other equation and solve for the remaining variable.
  3. Substitute back to find the other variable.

Let's start with the equations:

  1. \( Y = -4x \)
  2. \( Y = 3x + 28 \)

Since both equations are equal to \( Y \), we can set them equal to each other:

\[ -4x = 3x + 28 \]

Now, we'll solve for \( x \).

  1. Add \( 4x \) to both sides:

\[ 0 = 3x + 4x + 28 \]

\[ 0 = 7x + 28 \]

  1. Subtract \( 28 \) from both sides:

\[ -28 = 7x \]

  1. Divide by \( 7 \):

\[ x = -4 \]

Now that we have \( x \), we substitute it back into one of the original equations to find \( Y \). We'll use \( Y = -4x \):

\[ Y = -4(-4) \]

\[ Y = 16 \]

Thus, the solution to the system of equations is:

\[ (x, Y) = (-4, 16) \]

So the final answer is:

\[ \boxed{(-4, 16)} \]